Threshold theorem in quantum annealing with deterministic analog control errors

TL;DR

This paper analyzes how deterministic analog control errors affect quantum annealing, providing bounds on state deviations and conditions under which accurate final states can be achieved with minimal measurements.

Contribution

It introduces a formal framework for modeling deterministic analog control errors and proves that under certain error bounds, the final quantum state can be reliably obtained.

Findings

Bound on the state deviation due to control errors

Final state can be accurately obtained with limited measurements

Error strength less than inverse of computation time ensures reliability

Abstract

We investigate the effect of deterministic analog control errors in the time-dependent Hamiltonian on isolated quantum dynamics. Deterministic analog control errors are formulated as time-dependent operators in the Schrodinger equation. We give an upper bound on the distance between two states in time evolution with and without deterministic analog control errors. As a result, we prove that, if the strength of deterministic analog control errors is less than the inverse of computational time, the final state in quantum dynamics without deterministic analog control errors can be obtained through a constant-order number of measurements in quantum dynamics with deterministic analog control errors.